Assuming that, in fast Fourier transform (FFT), T0 (s) denotes a time window length, fs(Hz) denotes a sampling frequency, and N (N is an integer of a power of 2) denotes a sampling number, the following relationship is established.T0=N/fs  [Formula 1]The time window length has a reciprocal f0 (Hz) called a frequency resolution, and satisfies the following relationship.f0=1/T0  [Formula 2]
When a signal wave is frequency-analyzed by means of FFT, a time window length corresponds to a time length of the signal wave to be subject to FFT, a frequency resolution corresponds to a minimum resolution of the frequency of the signal wave, i.e. frequency detection accuracy. Hereinafter, this time window length will also be referred to as “period for cutting out a signal wave to be subject to FFT”, “a period of a signal wave to be subject to FFT”, or the like. [Formula 2] indicates that a time window length and a frequency resolution in FFT have a conflicting relationship. This conflicting relationship is significantly effective on a frequency having a small frequency resolution. In a case where a frequency resolution of 0.01 (Hz) is required, a signal wave for 100 (s) as a reciprocal thereof needs to be subject to FFT. If a signal wave to be subject to FFT has a period of 0.01 (s), there is only obtained a frequency resolution of 100 (Hz) as a reciprocal thereof.
This conflicting relationship is possibly a constraint on FFT application, and various measures have been taken to avoid the constraint of the conflicting relationship. There is a conceivable method for applying FFT to a received signal wave and obtaining a peak frequency configuring a spectrum appearing in a frequency domain, and the method includes fixing a time window length T0 to a predetermined value, applying FFT to each of periods cut out so as not to be overlapped with each other at intervals T0 from the received signal wave (in other words, applying FFT a plurality of times), and averaging a plurality of obtained peak frequencies. This method occasionally achieves calculation of a peak frequency at a resolution higher than a frequency resolution f0 obtained by FFT performed once (at small frequency intervals). However, increase in the number of FFT application causes a problem of a longer period for cutting out a signal wave to be subject to FFT in proportion to the number of cutting out times.
When FFT is applied to a digital data string, there are obtained power spectra provided with amplitude values at constant frequency intervals from 0 to N−1 (equal to the frequency resolution f0) relative to a number N of samples to be subject to FFT. A frequency corresponding to the maximum power spectrum out of these power spectra will be called a peak frequency. The maximum power spectrum is specified by comparing each of the power spectra from 1 to N/2, for example, in accordance with a known method. In a case where the maximum power spectrum is obtained at a point p, a peak frequency fpk is expressed as fpk=p×f0.
Patent Literature 1 describes a method of obtaining a peak frequency while satisfying both a frequency resolution of 12 (Hz) or less and a period for cutting out a signal wave to be subject to FFT of 10 (ms) (corresponding to a underwater position resolution of 7.5 m) or less (See [0023] to [0026] and [0089] to [0090] in this literature. Note that the period for cutting out an input signal wave changes to 5 (ms) as an exemplary numerical value from [0097], although a reason therefor is unknown.). When the frequency resolution of 12 (Hz) is prioritized, the cutting out period is obtained as 1/12 (Hz)=83.3 (ms) in accordance with [Formula 2]. The number N of samples to be subject to FFT is required to be a power of 2. According to the literature, the signal cutting out period is set to 102.4 (ms) corresponding to N=1024 (see [0055] in the literature). In order to set a period for cutting out an input signal wave to be subject to FFT to 102.4 (ms), a period of 5 (ms) for obtaining actual data is insufficient and data of zero value is added to a section for an insufficient period 102.4−5=97.4 (ms). A data string obtained by adding the data of zero value (a section for a time length of 102.4 (ms)) is subject to FFT to obtain a peak frequency (see [0103] in the literature).
According to the method described in the literature, an effective data string included in the data string to be subject to FFT is only about 1/10 of the entire data string (about 1/20 according to [0103] in the literature). If a digital band pass filter (a digital BPF 62 in FIG. 7 of the literature), which is applied to a digital signal wave obtained by A/D conversion typically performed in a case where an input signal wave is an analog signal wave, is set to have a high degree and a narrow band, a signal having passed through the digital band pass filter is weakened and the volume of effective data decreases. The digital band pass filter is thus required to have a weaker filter property. The literature includes no recognition of a potential problem that it is difficult to avoid a negative influence by disturbance noise with an input signal wave having a short time length, and thus neither suggests nor teaches any solution to such a potential problem.
According to the literature, the digital signal wave (digital data string) to be subject to FFT includes actual data only in a section for about 1/10 (or about 1/20) of a required time window length for FFT application, so that many power spectra should be generated. When an actual signal wave to be subject to FFT includes disturbance noise, more excessive spectra will appear in the vicinity of a peak frequency. In this case, it may be difficult to specify the peak frequency.
Although various efforts have been made in order to avoid the constraint of the conflicting relationship upon obtaining a peak frequency of an input signal, there has not yet been found any universal solution.